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| Henrici P. — Applied and Computational Complex Analysis (Vol. 2) |
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| Предметный указатель |
Geometric series, terminating 584
Goursat, quadratic transformation of 166 438
Growth indicator 200 209 309
Growth parameter of function of exponential type 305 306
Growth parameter of function of semi-exponential type 315
Growth, bounded exponential 220 221
Growth, exponential 389
GVF 585 596 602
Haar’s lemma 287 288
Hadamard polynomial 527 600
Hadamard product 335
Hamburger’s representation 590 593
Hankel determinant 518 549 597
Hankel function 346 388 394 395 422 424 426 632
Hankel function, product of 396
Hankel function, Sommerfeld’s integrals for 346 347
Hankel’s integral, for gamma function 35 349 439
Hardy’s theorem on Laplace transforms 248 251 256 306 307 310
Hashing 406
Heat equation 237 246 341
Heaviside expansion theorem 280 281 282 291
Heaviside unit function 210 216 237 278
Heine — Borel lemma 532 563
Helly’s selection principle 575 578 587
Helly’s theorem 573 587
Helmholtz equation 344
Herglotz representation theorem 586 588
Hermite polynomial 443
Heun, equation of 164 193
Hille’s expansion 258
Horner rule 515
Hull, convex 311
Hull, convex of singularities 311 312 313 314 319 320 322 325 327 328 330
Hurwitz alternant 555 556 557 558 559 560
Hurwitz criterion, for stability 559
Hurwitz, theorem of 515
Hypothesis  120 121 123 124
Ikehara — Wiener theorem 290 300
Image function 199
Image function, asymptotic behavior of 290
Impedance 235
Implicit function theorem 418
Impulse 216 232 233 238
Inclusion region 614 626
Indicator function 309 312 314
Indicator function of exponential type 321
Indicator function of semi-exponential type 315 329
Infinite series, equivalent to  fraction 527
Initial value problem, for linear system 92
Input 227 229 232 242
Integral equation 382
Integral of Riemann 437 569 572
Integral of Stieltjes 569 570 572 573 581 585 609 641
Integral, n times repeated 30
Integral, of Mellin — Barnes type 62 65 66 69 74 320
Integration, numerical 457 467
Integration, numerical, of original function 214
Interpolation formula, of Lagrange 196
Inversion formula for discrete Laplace transform 328 333
Inversion formula for functions of exponential type 308
Inversion formula of Stieltjes — Perron 591 594
Inversion formula, complex 277 278 279 288 308 471
Inversion formula, real 282 284
Inversion, of Laplace transform 222
Irrationality, quadratic 494 499 639
J fraction 529
Jacobi distribution 618
Jacobi polynomial 163 450 618 619
Jacobian matrix 78
Jacobi’s identity for theta function 272 305
Jacobi’s identity, for Hankel determinants 550
Jacobi’s triple product identity 12 13 16 73
Jordan canonical form 1 20 537
Jordan’s lemma 279 281 284
Jordan’s test, for condition (C) 267
Kapteyn series 431
Keplerian motion 113
Kernel 381 382 383
Khintchin’s constant 640
Kummer, first identity of 71 135 136 142
Kummer, second identity of 72 137
Kummer’s equation 132 134 135 142 180 190
Kummer’s formula, for sum of hypergeometric series 50 51
Kummer’s function, asymptotic representation of 357
Lagrange — Burmann formula 399 401
Laguerre distribution 622 632
Laguerre polynomial 257 259 260 443 623 624 629
Landau’s O-symbol 286 354
Laplace integral 200 202
Laplace integral, asymptotic behavior of 389
Laplace transform 199 279 389 629
Laplace transform of function of exponential type 306
Laplace transform, analytic continuation of 310
Laplace transform, applications, to partial differential equations 340
Laplace transform, behavior at infinity 205
Laplace transform, considered as Fourier transform 276
Laplace transform, discrete 198 321
Laplace transform, iterated 627
Laplace transformation 197 198 199
Laplace transformation, inverse 232
Laplace transformation, inversion of 337
Laplace transformation, inversion of, by expansion in Laguerre polynomials 258
Laplace transformation, inversion of, by Fourier integral theorem 261
Laplace transformation, inversion of, by Hardy’s theorem 256
Laplace transformation, tables of correspondences for 350
Laplace transformation, two-sided 336
Laplace’s equation 174 342 343
Laplace’s method, in asymptotic theory 407
Laurent series 12 45 70 117 118 147 368 369 370 566
Laurent series, formal 115 127
Leau — Wigert — Polya theorem 327
Lebesgue integral 258 270
Legendre function 121 165 174 175 620
Legendre function of second kind 175 440
Legendre polynomial 175 176 443 619
Legendre polynomial, asymptotic behavior of 403 438
Legendre, differential equation of 172
Leibniz criterion 295 484
Lemniscate constant 62 73 74
Lerch, formula of 55
Lerch, theorem of 208
Light bulb 246
Limit, numerical evaluation of 461
Line, critical 387
Linearity, of Laplace transform 210
Liouville’s theorem 43
Logarithm 467 533 619 639
Logarithmic sum, formal 115 117 118 128 129
Logarithmic sum, reduced 116
Lommel polynomial 550
Majorants, method of 88 91 93
Matrix differential equation 95
Matrix, circulant 415
Matrix, formal logarithmic 116
Matrix, Hessean 409 414
Matrix, log-exponential 182 183 186
Matrix, norm of 78
Matrix, sparse 538
Matrix, trace of 96
Mean, arithmetic-geometric 177 178
Mean, arithmetic-geometric, modified 179 180
Mellin inversion formula 338 343
Mellin transform 337
Mellin transform, inversion of 338
Mellin transform, operational rules for 338
Mellin — Barnes integral 62 65 66 69 74 230
Method, symbolic 195 197
Miller, J. C. P., formula of 403
Mill’s ratio 640
Minkowski’s inequality 603 606 615
| Mittag — Leffler function 333
Modulus of continuity 571 574 579
Moebius symbol 304
Moebius transformation 151 152 165 168 473 474 477 479 488 490 497 515 524 588 609 612 613
Moebius transformation, matrix associated with 477 497 504
moment 582 583 595 598 624
Moment problem 635 636 637 638 639 640 641
Moment sequence 602
Monodromy theorem 94 107
Montcl’s theorem 563 564
Multiplication, of original function 213
Nevanlinna representation formula 588 594
Norm of matrix 78
Norm of subdivision 569
Norm of vector 75 78
Number, algebraic 494
Number, irrational 491 492 493
Number, rational 489
Numerator, of continued fraction 477 479 490 491 498 501 512 516 525 532 537 542 560 561 598
Numerator, of continued fraction, partial 474 480 525 540
numerical 279 350
Nyquist diagram 231
Operational calculus 197 212 234
Original function 199 389
Original function, asymptotic behavior of 289
Original function, order of magnitude of 286 288
Original space 199 627
Output 227 229 238
P symbol, of Riemann 151 157
Padd table 524 640
Painlevd, equation of 193
Parabola theorem 514
Parameter, accessory 164
Parameter, analytic dependence on 81
Parameter, differentiation with respect to 127 129
Parseval’s formula 270 275 292
Partial fractions 146 195 198 223 224 226 445 446 460 553 554 561 565 585 637
Partial sum, symmetric 264
Partition 9 11 14
Partition function 9 14
Path, steepest 417
Pell’s equation 499 500 501
Pendulum 233 236 242.
Periodic function, Laplace transform of 216
Perron — Pringsheim theorem 508 532
Perron’s formula 304
Pincherle’s theorem 308 320
Pivotal point 569 571
Plana summation formula 38 300 329 330
Pochhammer symbol 26 68
Pochhammer, loop integrals of 57 58 59 60
Point of discontinuity, of non-decreasing function 576
Point of increase 579 580 594 597
Poisson summation formula 270 271 272 273 274 276 322 350
Poisson’s integral, for Bessel function 142 244 273
Pole 105 368 370
Polya’s formula, for discrete Laplace transform 322 328 329
Polya’s theorem, on functions of exponential type 312 316
Polynomial of Chebyshev 176\
Polynomial, characteristic 195 221
Polynomial, exponential 223 226 282
Polynomial, indicial 127 147
Polynomial, of Legendre 175 176 403 438
Polynomial, orthogonal 600 618 623 641
Polynomial, stable 555 559 641
Polynomial, ultraspherical 440 443 448 449
Power function, fractional 247
Power series in two variables 85
Power series, asymptotic 351 361 530 582
Power series, asymptotic, algebra of 362
Power series, asymptotic, analytic properties of 368
Power series, asymptotic, composition of 364
Power series, asymptotic, differentiation of 372 375 376
Power series, asymptotic, integration of 372 374
Power series, asymptotic, numerical use of 396
Power series, asymptotic, summing of 371
Power series, asymptotic, uniqueness of 357
Power series, corresponding 565
Power series, formal integral of 372
Power series, noncontinuable 314
Power series, normal 523 524 526
Power series, represents function asymptotically 355 357 359
Prime factor 15
Prime number 16
Prime number theorem 302
Principal part 281
Principal value 278 281
Principal value integral 268 288
probability density 471
Product of Vieta 6
Product, absolutely convergent 4
Product, canonical 22 24
Product, conditionally convergent 6 36
Product, infinite 1 466 471 474
Product, infinite, combinatorial interpretation of 7 8 11 14
Product, infinite, convergence of 1 2
Product, infinite, relevant to number theory 7 15
Product, infinite, special 46—54
Product, infinite, uniformly convergent 4 19
Product, partial 1 6 13 15 46
PSA 586 588 594 596 608
Pseudofunction 232
qd algorithm 519 528 539
qd algorithm, incremental version of 632
qd scheme 526 597 617 622 624 625 633 634 639
Quadratic irrationality 494 499 639
Quadratic irrationality, conjugate 498 499
Quotient field 197
Quotient-difference scheme see “qd scheme”
Ramanujan, formula of 61
Rate of convergence, subgeometric 624
Rational function, positive symmetric 553 555
Recurrence relation 471
Region, circular 503 507 610 611
Renewal equation 245 246 350
Residue 27 52 53 54 64 65 67 69 70 145 278 280 289 322 365 553
Residue of formal Laurent series 400 402 404 421
Resistence, symbolic 235
Response 227 232 238
Response, steady-state 231
Reversion, of formal series 367
Rhombus rule 527
Riemann sphere 145
Riemann surface 108
Riemann — Lebesgue lemma 263 265 266 268 269 277 288 350
Riemann, method of 156
Riemann’s conjecture 303 304 305
Riemann’s integral 437 569 572
Riemann’s integral for hypergeometric function 57 621
Riemann’s theorem 369
Right component 323
RIT transformation 474 479 516
Ritt’s theorem, on asymptotic series 371 379 472
RITZ fraction 515 516 518 519 522 523 524 530 539 540 541 542 544 549 550 551 552 557 559 561 618
RITZ fraction, convergence of 529
RITZ fraction, corresponding to exponential series 538
RITZ fraction, n-terminating 545 546 548
RITZ fraction, rational 545
Romberg algorithm 274 275 461 463 467 470 472
Romberg array 463 466 469
Romberg array, diagonals of 464
Romberg scheme see “Romberg array”
Routh algorithm 231 547 548
Routh scheme 557 558
Rules, operational, for Laplace transform 209—218
Runge and Kutta, formulas of 91
S fraction 561 562 564 568. 578 579 585 596 626. 632
Saddle point 417 419 420 422 423 425 428 471
Saddle point, order of 429
Saff — Varga theorem 514 640
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